The Etherwave Pro is the only instrument which I have experienced this excellent linear interaction of which I've described. After the past year of studying this particular aspect of the theremin, I am inclined to think that linearity plotted on a graph is only useful to the person who created the graph.
I can speak much more about my theories. I just don't want to write it all in one post because there is a lot to be said.
From the players side of the equation, I have isolated two variables: 1) Proximity of the hand (towards the pitch antenna) and 2) overall capacitance (defined by the total surface area of the players body, including any objects connected to the body, for example sitting on a chair, and also to some degree the capacitance of the surrounding walls, ceiling, floor, air)
The proximity variable can be detected easily. it's the theoretic 'overall capacitance' variable that is the mysterious one because it is unique to each player/environment. In my opinion, it has been a huge mistake for the second variable to be omitted from the equation, but a huge problem exists, as it is very difficult to measure this value.
As I understand now, there are two equations that must be balanced in order to obtain a linear interaction. The theremin must first first respond to changes in capacitance in a linear function... this is, of course, a result of the great work of the engineering of a theremin circuit. However ... A second equation must also yield a linear response in order for the theremin to actually produce the linear change in pitch that was intended by the engineering. The second (what seems to be unconsidered) equation is: the change in capacitance created by a linear difference of the hand position changing in proximity against the overall capacitance value.
This is the reason I believe the theremin cabinet design has an effect on linearity... not because it has anything to do with what goes on inside the theremin, but because it affects the external equation as the physical material in the cabinet becomes part of the changing capacitance value. This means that at any give location of the hand in the field, all materials at the same proximity are averaged into the capacitance value. not only that, but anything connected to these objects (within a given proximity) also have an influence : the human body attached to the arm, and the room capacitance to a lesser degree.
I had a very deep discussion of all these topics with Dan Burns, and we agreed on all points. Most of his B3 theremins have a retractable antenna. With the B3 that I owned I experimented quite extensively with this added variable. In the end I was able to tweak the pitch response to achieve a two octave portion of the range that offered the kind of linearity that I wanted. i tuned the total playable range to be about 3.5 octaves, but only the inner two gave me the linear response. the full range was actually 6 octaves, but due to the physical size of the range I wanted, the outermost 2.5 octaves were extremely non-linear.
My hypothesis, is that I balanced out the two equations (the internal, and external) by adjusting the antenna's surface area.
If the surface area of the pitch antenna can be defined to a greater degree, as was/is the case with the Henk theremin, it offers a way to balance out the equation on the theremin player side in a larger space. This is my impression of what happens. There could be some other logical conclusion, but because I experienced the same effect on the B3, it is the conclusion I have arrived to.
With the Henk, there is a much bigger antenna, extendable to a greater degree... What I imagine is happening is that : the person/environment has an overall capacitance at rest (meaning no moving objects, nothing changing) and the surface area of the antenna dictates what that value will be... the greater the surface area, I would think, would yield a higher capacitance value from the environment.
the obvious values to measure have traditionally been proximity of the hand, and resulting change in pitch. But I think perhaps that because the overall capacitance values and antenna surface area are difficult to measure it may not be easy to place them into an equation.
I made a crude diagram that I used to help explain these concepts to the engineer in Seattle that I am working with. I'll redraw it for readability and post here soon... I also have thrown a new variable into the mix in the player side equation... I get into that in another post.
I have more to share, but I think I need to know if what I've said already makes sense from an engineering point of view. please share impressions, dewster, chobbs, FredM, Thierry, Christopher, or whom ever wants to jump in.
Clara Rockmore spoke of "thereminists today" from her period of time. Her statement does not apply in 2013, while we are in a time of great accessibility, where there are more than enough passionate individuals who are pushing the envelope to extend what has previously been possible. I stopped listening to much of Clara's advice because IMO if she were here today, she wouldn't be saying such things.